Example high-dimensional survival data

A simulated high-dimensional survival dataset under a linear Cox model with 50 covariates (6 signals + 44 noise variables), a Weibull baseline hazard, and controlled censoring. The dataset includes internal train/test samples and multiple externally estimated coefficient vectors representing different forms of coefficient perturbation.

Usage

data(ExampleData_highdim)

Format

A list with the following components:

train

A list containing:

z

A data frame of dimension \(n_{\mathrm{train}} \times 50\) containing covariates Z1–Z50.

status

A numeric vector of event indicators (1=event, 0=censored).

time

A numeric vector of observed survival times \(\min(T, C)\).

stratum

A vector of stratum labels (here all equal to 1).

test

A list with the same structure as train, with covariates of dimension \(n_{\mathrm{test}} \times 50\).

beta_external

A numeric vector of length 50 (named Z1–Z50) containing Cox regression coefficients estimated from an external dataset using only Z1–Z6, with zeros for Z7–Z50.

beta_external.multi1

External coefficient vector with additive Gaussian noise applied to the nonzero entries of beta_external, preserving the original sparsity pattern.

beta_external.multi2

External coefficient vector with weak Gaussian noise applied to all 50 coefficients, yielding a dense but low-magnitude perturbation.

beta_external.multi3

A scaled version of beta_external with uniformly attenuated signal strength.

beta_external.multi4

External coefficient vector in which a subset of the nonzero coefficients in beta_external have their signs randomly flipped.

beta_external.multi5

External coefficient vector with weakened original signals and a small number of newly introduced weak signals among previously zero coefficients.

Details

Data-generating mechanism:

• Covariates: 50 covariates with true signals in Z1–Z6 and noise variables in Z7–Z50.

  • Z1, Z2: bivariate normal with AR(1) correlation \(\rho = 0.5\).

  • Z3, Z4: independent Bernoulli(0.5).

  • Z5 \(\sim N(2, 1)\), Z6 \(\sim N(-2, 1)\).

  • Z7–Z50: multivariate normal with AR(1) correlation \(\rho = 0.5\).

• True coefficients: \(\beta = (0.3, -0.3, 0.3, -0.3, 0.3, -0.3, 0, \ldots, 0)\).

• Event times: Weibull baseline hazard \(h_0(t) = \lambda \nu t^{\nu - 1}\) with \(\lambda = 1\) and \(\nu = 2\). Given linear predictor \(\eta = Z^\top \beta\), event times are generated as $$T = \left(\frac{-\log U}{\lambda e^{\eta}}\right)^{1/\nu}, \quad U \sim \mathrm{Unif}(0,1).$$

• Censoring: \(C \sim \mathrm{Unif}(0, \mathrm{ub})\), where ub is tuned to achieve the target censoring rate (internal: 0.70; external: 0.50). The observed time is \(\min(T, C)\) with event indicator \(\mathbf{1}\{T \le C\}\).

• External coefficients: Cox regression models with Breslow ties are fitted on the external dataset using Z1–Z6. The resulting estimates are embedded into length-50 coefficient vectors, with additional variants constructed to represent different forms of coefficient perturbation and distributional shift.

Examples

data(ExampleData_highdim)